1. Simulation of Heavy Ion Beam Propagation D. R. Welch and D. V. Rose Mission Research Corporation, Albuquerque NM C. L. Olson Sandia National Laboratories Simon Yu Lawrence Berkeley National Laboratory P. F. Ottinger Naval Research Laboratory Presented at the ARIES Project Meeting 6-7-01

2. Outline of Talk Assisted-Pinch Transport –concept –self field evolution –transport efficiency –stability Self-Pinched Transport –concept –pinch force mechanism –propagation window –status of 3d modeling Transport Issues

3. IPROP Modeling of Assisted Pinch Transport EquilibriumStability

4. ~ 5 Torr Xe Z-Pinch Stable? Z-Pinch Stable? ~50 kA Return path/ channel interaction ? Return path/ channel interaction ? Breakdown to Walls? Channel transport could ease chamber focus requirements and reduce driver costs Laser

5. Key physics issues involve the evolution of self fields Beam must first be captured at small radius by 50 kA discharge current - adiabatic lens 6-MA electrical beam current has potential for huge self fields given finite plasma conductivity Strong plasma return current can drive “hose” instability

6. IPROP * simulates HIF beam interaction with discharge channel in 2 and 3D IPROP is a quasi 3D EM hybrid code 2 fluid model for the plasma, PIC beam ions Extensive models for xenon gas breakdown physics * D. R. Welch, et al., Phys. Plasmas 1 (1994) 764.

7. Simulation beam and gas conditions 4-GeV, 6 MA Pb +72 ions 15-cm radius beam is first transported ballistically 10 meters to the discharge. Micro-divergence nominally 1 mrad. Discharge initial parameters: 50-kA current 5-Torr, 3-eV ambient Xe Axial position-dependent radius, reduced density (to 0.5 Torr minimum), ionization fraction (0.9 peak). Current density, reduced gas density and ionization fraction have square profiles Pb +72 10 m 15 cm ballistic transport Adiabatic lens Chamber entrance

8. Effective current - sum of discharge and self currents - reaches 80 kA Results for nominal parameters 6 snapshots of effective current 2-4  s plasma return current decay time permits self field growth Beam at snapshots

9. Plasma heats ohmicly and from beam impact - decay time increases Red contour is 3.3 keV, beam head at 375 cm Enhanced sigma reduces magnitude of B oscillation Enhanced heating at beam waists

10. Beam oscillations imprinted on self magnetic fields

11. Beam halo growth from interaction with varying B  (z) 87% of beam transported over 4.5-m length 3.5-mm RMS radius

12. Finite conductivity results in some self field growth, beam loss Plasma current decay time scales as  r 2, reaches 2- 4  s (enough to permit 20-30 kA self field for 8 ns beam) Inductive fields rise with net current, reducing beam energy Oscillating beam imprints oscillating magnetic well Ions interact with changing B fields and heat Despite above effects, 87% beam energy transported, 3.5-mm RMS radius.

13. IPROP is run with 2 azimuthal Fourier modes, m=0,1 Beam is injected offset from channel 0.5 mm Conductivity profile is held fixed by initializing a singly ionized plasma with a gaussian radial profile Fixed plasma  profile Run91 - 100 eV plasma and 50 kA discharge Run92 - 10 eV plasma and 50 kA discharge Run93 - 30 eV plasma and 12.5 kA discharge IPROP simulations of assisted-pinch hose instability

14. Nominal conductivity simulation shows no evidence of hose Fixed 5 microsecond decay time - consistent with 2D breakdown calculations 100 eV plasma temperature 50 kA discharge offsets damp

15. Highly resistive case - less than an e-fold growth 10-eV temperature, 50 kA discharge Large net currents, beam pinches Weak hose growth that damps rapidly

16. Low discharge current, medium conductivity case 30 eV temperature, 12.5-kA channel Hose again is very weak

17. Simulations suggest weak assisted pinch hose Hose instability does not appear to be an issue for assisted pinch Neglected effects of beam scattering, ionization should be stabilizing * Ed Lee’s stability condition from Pinch Transport Workshop, 2001 I d dp / (I b b ) > 1* IPROP result ____________________________________________ run915rock stable run920.4weak instability run930.26weak instability

18. Optimization of beam transport - work in progress Self-field strength limits energy transport efficiency and spot size 87% transport and 3.5 mm RMS spot size calculated over 4.5-m transport Weak self-hose instability calculated Need to develop technique for hollowing beam profile to better match recent target designs

19. LSP Modeling of Self-Pinched Transport Propagation of pinched beam

20. 2 possible scenarios for self pinched transport Beams combined into 2 as in assisted pinch –large currents have potential for instability without discharge channel Use 100-200 beams with 1-4 kA per beam (as in Neutralized Ballistic Transport) –requires more beam ports, beams overlap near target Graphic provided by P. Peterson, UCB

21. Self-pinched transport relies on limited beam impact ionization in a low pressure gas Ionization electrons provide good charge but imperfect current neutralization  v b   v bz B lab frame B IbIb + - + - + - - - wall foil - c

22. Self-pinched transport is predicted to occur at an intermediate gas pressure Maximum pinch force occurs when beam-impact ionizes a plasma density roughly that of the beam on time-scale of beam density rise time, /v b Optimized for: R =  n g /4Z =1 * Trumpet shape and non- local secondary ionization help supply neutralization without v e = v b * D.R. Welch and C.L. Olson, Fus. Eng. and Des. 32-33, 477 (1996). - + Beam - + E E B B lab frame c Electron orbits are mainly ExB

23. Simulations indicated that a large net current fraction can be generated for SPT of a 1.5-MeV, 50-kA proton beam 1.5 MeV protons I b = 50 kA r b = 2.8 cm   = 53 mrad Consistent with results observed in SPT experiment on Gamble II at NRL (Ottinger et al., Phys. of Plasmas 7, 346, 2000)

24. Identify pinched transport gas/plasma constraints for HIF chamber transport New LSP * code calculations 10-kA, 4-GeV Pb + beam, 2-ns rise in current = 2 ns trumpet-shaped beam envelope: –1-cm max radius falling to.5 cm in 2 ns 3-300-mtorr FLiBe pressure (R =.1-10) Normalized plasma density N = n p /n b =0-1 –n b = 1.3x10 13 cm -3 Beam impact ionization only (ignore avalanche) * Welch, et al., Nucl. Instrum. Meth. Phys. Res. A 464, 134 (2001).

25. Weak net force for pencil beam in gas Significant fields limited to beam edge (skin depth effect) Constant enclosed net currentElectric fields, 918 kV/cm max beam density

26. Trumpet beam shape enlarges net-current sheath Large net current with trumpet Sheath thickness defined in low density beam front Constant enclosed net currentElectric fields, 529 kV/cm max

27. Electron density follows trumpet shape Ion density indicates ionization position Log plasma ion densityLog electron density Log beam density

28. LSP calculates strength of pinch force sensitive to gas, plasma densities Normalized gas density, R =  n g /4Z Normalized plasma density (R=1), N = n p / n b Pinch force optimized near R = 1-2, constrains chamber pressure Falls off N > 0.1, pinch may weaken near target due to photo-ionization

29. Beam Density contours (cm -3 ) 30-mtorr flibe R = 1, F = 0 4 ns9 ns 15 ns Beam maintains pinch after detaching from wall

30. Pinch force stabilizes at 3 kA in meter long simulation Pinch force is still sufficient for confinement Electric fields are small, < 100 kV/cm

31. Two-beam interaction in 3-D LSP simulation geometry Pb +5, 4 kA (electrical) current, n p = 5e13 cm -3, n b = 1e12 cm -3

32. No observed deflection for these 2 weak beams in N=10 plasma Need to examine higher currents, ionization and lower plasma densities

33. Research in self-pinched transport for HIF beams has just begun Confirmed the SPT mechanism for HIF beams –constraints of gas pressure and plasma density Pinch is sustained after detachment from wall Simulation of 3d beam-beam interaction underway Many issues remain: –Detailed beam-gas interaction (such as beam stripping) –Beam losses from inductive fields, trumpet formation –m=1 (hose) stability, beam-beam interactions –Steering and capturing beam –Channel expansion from JxB force